Black Holes in (Quartic) Quasitopological Gravity

TL;DR

This paper introduces quartic quasitopological gravity, constructs explicit black hole solutions in higher dimensions, and analyzes their thermodynamics, extending the understanding of curvature-coupled gravity theories beyond previous models.

Contribution

It develops a new quartic quasitopological gravity theory with second order equations and provides explicit black hole solutions in various dimensions, analyzing their thermodynamic properties.

Findings

Unique black hole solutions in dimensions >4, except 8.

Entropy calculations as a function of horizon radius.

General remarks on higher-order quasitopological gravity.

Abstract

We construct quartic quasitopological gravity, a theory of gravity containing terms quartic in the curvature that yields second order differential equations in the spherically symmetric case. Up to a term proportional to the quartic term in Lovelock gravity we find a unique solution for this quartic case, valid in any dimensionality larger than 4 except 8. This case is the highest degree of curvature coupling for which explicit black hole solutions can be constructed, and we obtain and analyze the various black hole solutions that emerge from the field equations in $(n+1)$ dimensions. We discuss the thermodynamics of these black holes and compute their entropy as a function of the horizon radius. We then make some general remarks about $K$-th order quasitopological gravity, and point out that the basic structure of the solutions will be the same in any dimensionality for general $K$ apart from particular cases.